37 items are filed under this topic.








A pattern rule for a sequence 
20161028 

From Grace: Here's a Grade 7 question, we need to find the pattern rule:
1  1
2  3
3  6
4  10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace. Answered by Penny Nom. 





Two sequences 
20160820 

From Ting: The first four terms of a sequence are 4, 20, 56 and 120. By comparing with the nth term of sequence 1,5,14 and 30 which is 1/6n(n+1)(2n+1), find a formula for nth term. Can you precisely show out how you do this questions ( with the steps please) Answered by Penny Nom. 





Some nondecreasing sequences 
20150413 

From Sky: Hi I'm a Student and i'll try my best to state the problem perfectly.
The number of nondecreasing sequences of size at least 1 and at most N,
such that each element of the sequence lies between L and R, both inclusive.
Eg: N=1 L=4 R=5
ans= 2. [{4},{5}]
N=3 L=4 R=6
ans= 19. [{4},{5},{6},{4,4},{4,5},{4,6},{5,5},{5,6},{6,6}
{4,4,4},{4,4,5},{4,4,6},{4,5,5},{4,5,6},{4,6,6},{5,5,5},{5,5,6},{5,6,6}
,{6,6,6}] Answered by Claude Tardif. 





A sequence 
20090919 

From Oliver: I am struggling to work out the missing terms in the following sequence:
1, 3, _, 7, 11, 18, _ Answered by Chris Fisher. 





Successive differences 
20090618 

From Jonathan: I'm trying to find the next number sequence for this equation: 1 11 35 79 149 251, my problem is that I worked it out and ended up with a single number 17. What am I doing wrong. Thank you for any help. Answered by Robert Dawson and Penny Nom. 





Jon's bank account 
20090103 

From Abigail: Hi, i have an exam soon (monday =[ )
in my revison book, it shows two peoples bank accounts and then it says
"write a formula to show the balence of Jon's bank account after n weeks of 2003"
this is the table show
Jon's Bank account
Weeks 
Week 1 
Week 2 
Week 3 
Week 4 
Week 5 
Balance(£) 
970 
1035 
1100 
1165 
1230 
Answered by Penny Nom. 





0.151515...=15/99 
20080908 

From Emma: This week, my Algebra teacher told us about the pattern between infinitely repeating
decimals and their corresponding fractions.
(ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.)
I was just wondering the reason why this pattern occurs.
Is there a certain element that causes this pattern to occur?
Thanks
Emma Answered by Penny Nom. 





Practical applications of sequences 
20080101 

From carl: can you give me examples of different kinds of practical applications of sequences? Answered by Penny Nom. 





Two sequences 
20071114 

From Kim: Pattern........what comes next?
1,4,9,16,25,_____,____
1,4,9,16,27,40,__________,_______ Answered by Penny Nom and Gabe Potter. 





The nth term 
20061214 

From Hepzibah: what is the definition of nth term and n? Answered by Penny Nom. 





How many sequences are possible? 
20061028 

From Sam: A fair eightfaced die with faces numbered 1,2,3,4,5,6,7 and 8 is tossed six times and the sequence of numbers is recorded. How many sequences are possible? Answered by Penny Nom. 





Arithmetic progressions 
20060131 

From A student: 1)the sum to n terms of a particular series is given by S_{n}=17n3n^{2}
a)find an expression for the n term of the series
b)show that the series is an arithmetic progression
2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference
Answered by Penny Nom. 





A sequence of circles and tangents 
20060116 

From Paul: Consider a circle whose center is (2,2) and whose radius is 1, and the
straight line that goes through the origin and that is tangent to this
circle so that the intersection between them is as shown in the attached
picture. With this new point we make a new circle whose radius is half
of the first one, and we calculate the corresponding intersection point
with the same suppositions as in the first case. We repeat the process
to the infinite. Find the distance between the center of the circle in
the infinite and the origin (point (0,0)). Answered by Chris Fisher. 





Find the next 5 terms 
20050924 

From Grant: n+7, 2n0.5, 4n. Find the next 5 terms of each one and explain the sequence in words Answered by Penny Nom. 





Find the first five terms of this sequence? 
20050917 

From Jade: my homework says can you find the first five terms of this sequence?
5n6 i can`t figure it out. Answered by Penny Nom. 





Finding the nth term 
20050912 

From Paul:
Hi , Im having a problem helping my daughter to find the Nth Term in the following sequences.
1/3 1/2 3/5 2/3
and
1 3 6 10
Answered by Penny Nom. 





Geometric sequences 
20040203 

From Alan: hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative. Answered by Chris Fisher. 





The 4th difference 
20031117 

From Jack: If i had a sequence which was the same at the 4th difference, aka difference
to the 4th, like:
1 5 14 30 56 96
(sequence)
4 9 16 26 40
5 7 10 14
2 3 4
1 1
then what would be the set formulars to find out a, b, c, d, and e
as i know the equation has to be an^{4}+bn^{3}+cn^{2}+dn+e Answered by Penny Nom. 





Two sequences that agree in the first 4 terms 
20030526 

From A student: Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest? Answered by Penny Nom. 





Finite differences 
20030210 

From Jenny:
I need to find a formula that will work with any number. I am finding the volume of a 3d cross shape. Here are my results so far:
Term Number 0 1 2 3 4 5
nth term 1 7 25 63 129 231
1rst diff 6 18 38 66 102
2nd diff 12 20 28 36
3rd diff 8 8 8
I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. 





Sums of evens 
20020914 

From Rosa: How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + .... Answered by Leeanne Boehm and Harley Weston. 





What is the next term? 
20020621 

From A student: What is the next term in the sequence: 1, 5, 14, 30..... Answered by Penny Nom. 





Sequences that agree on their first four terms 
20020516 

From Mike: Are there two formulas that define sequences that agree on their first four terms, but differ on the fifth term and all succeeding terms? Answered by Chris Fisher. 





1,4,27,____,_____46656 
20020221 

From Brenda: 1,4,27,____,_____46656..... please find the fourth and fifth numbers in this sequence. Answered by Penny Nom. 





Number sequences 
20011117 

From Stephanie: My name is Stephanie. My grade 7 math class is studying number sequences and, to me, they make almost no sense at all. Here I wrote down 2 of the many problems I have for homework and was wondering if you could explain them to me (I have to find the next 3 numbers in each sequence.) It would be a big help! 10, 14, 18, 22, _, _, _. 12, 21, 39, 75, _, _, _. Answered by Penny Nom. 





Find the pattern 
20010926 

From A parent: MY SON HAD ON A WORKSHEET WHAT I HAVE LISTED BELOW, BUT WE CAN'T SEEM TO FIND THE PATTERN. MOST THE TIME WE CAN, BUT THIS ONE IS DIFFERENT. 6,___, 9,____,____,_____,_____,_____ Answered by Caude Tardif. 





Four sequences 
20010924 

From Nicole: I have a few questions I couldn't figure it out. So any help will be great to find the next three numbers or letters. Here's the patters...  DEGHNORY, EHILMU, HIILMTU, BEILLMRUY,...
 50, 33, 25, 20, 16, 14, 12,...
 1777, 1795, 1818, 1819, 1820, 1822, 1836, 1837..
 A,H,I,M,O,T,...
Answered by Chris Fisher and Penny Nom. 





Arithmetic sequences 
20010910 

From Rachel: I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting 9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given. Answered by Penny Nom. 





Geometric and arithmetic sequences 
20010126 

From Garry: what are the equations for geometric and arithmetic sequences? also, what are the equations for finding the sums of those series? Answered by Leeanne Boehm and Penny Nom. 





Some terms in a sequence 
20010115 

From jamie: Please help as soon as possible! i am stuck with some terms in a sequence. the terms are 1st term=1, 2nd term=10, 3rd term=35, 4th term=84, 5th term=165, 6th term=286. can anyone tell me the formula for the nth term? n is term number Answered by Sukanta Pati. 





The sum of the squares of 13 consecutive positive integers 
20000825 

From Wallace: Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square. Answered by Harley Weston. 





Covering 1, 1/2, 1/3,... 
20000822 

From Wallace: Consider the points 1, 1/2, 1/3, ... on the real number line. You are given five small bars, all of length p, which are to be placed on the number line such that all points will be covered. What is the minimum value of p that will allow you to do this? Answered by Penny Nom. 





Patterning and Sequencing 
20000705 

From Michael Jellis: What would be the next two terms? 1.0,0.5,0.6,0.75,0.8,___,____ please explain!!! I am completely baffled and need all the help I can get! Answered by Claude Tardif. 





A sequence 
20000616 

From Claire Hall: Can you find the formula for the pattern 4,12,24,40,60 Answered by AClaude Tardif. 





Geometric sequences 
20000411 

From Jodie: I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much! Answered by Harley Weston. 





Number sequences 
19991111 

From Justin Schessler: I CAN NOT figure out this sequence or how we continue this sequence... 3,2,6,5,15,14,___,___,___ Answered by Chris Fisher and Harley Weston. 





Where three sequences meet. 
19990306 

From Ali: My name is Ali and I am in the 5th grade. I have a math question: What is the least positive integer meeting each of the following conditions:  Dividing by 7 gives a remainder of 4
 Dividing by 8 gives a remainder of 5
 Dividing by 9 gives a remainder of 6
Help! Answered by Denis Hanson. 


